Time series are data observed over time (either in continuous time or at discrete time periods).

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How to calculate interim and long-run multipliers in ARDL models with >1 lag?

I have calculated an ARDL(24,36) model with 1 independent variable. The data is monthly, hence the inclusion of so many lags. I am trying to calculate the interim multiplier (the cumulative effect at ...
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26 views

How to use RMSE when having data normalization?

I am new in machine learning and I am studying time series prediction using neural networks. Pseudocode 1: ...
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28 views

Time series as stationary stochastic process

(This is a homework problem.) Check if the following series is covariance stationary: $$ \newcommand{\if}{\text{if }} Z_t = \begin{cases} X_t &\if t\text{ is even}, \\ ...
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1answer
42 views

Monte Carlo rolling forecast of time series - details needed

I know I'm doing a short term forecast of a volatile time series using Monte Carlo, but I'm unsure as to the details - for example, I'm sure I had a very good reason for naming a term 'drift', but I ...
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23 views

Time-series with RNN - how to deal with attributes that span entire sequences?

I am currently trying to train recurrent neural networks for time-series forecasting, and I'm having trouble figuring out how to properly deal with attributes that stay constant over each series. For ...
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2answers
76 views

Correcting autocorrelation with MA in a regression

I would need some advice on a multivariate regression problem. I am running regressions with macroeconomic data at first difference and using a AR(1) as regressor to correct autocorrelation (it makes ...
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52 views

What is this time series model and how to produce it in R?

I know that $Y_{t} = a + bY_{t-1} + \epsilon$ is named as autoregression model. I am dealing with the model like: $Y_{t} = a + bY_{t-1} + cX_{t} + dX_{t-1} + \epsilon$. I could not find any useful ...
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1answer
59 views

Testing significance of cross-correlated series

I want to prove that, overall, signal B is correlated to signal A. I was thinking of using cross-correlation (in R) to measure this. Essentially I have two kinds of signals: signal A is a series of ...
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37 views

(S)ARIMA — Hints with Time Series

I am a beginner in time series analysis and I would like discuss a couple of numerical examples here implemented in R. I am reading some interesting books, but I also need some expert advice to get ...
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13 views

How to find correlation of a response variable with multiple predictors for a time series data?

How do you find the correlation between a response variable and multiple predictors with time series data? I need to study the trend of a variable vs other variables for an entity.
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24 views

How can I test for seasonality when the trend is not supposed to be monotonic but sinusoidal?

My knowledge of time-series analysis is limited. So far I have only assessed whether there was a seasonality in my time series data with the assumption of monotonic trend. To test that I would have ...
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5 views

Is it possible to combine linear VAR restrictions with SVAR A/B restrictions?

I have been exploring the various restrictions that are commonly applied to (S)VAR models in textbooks on multivariate time series, noting that linear restrictions on VAR models seem to be treated ...
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43 views

How to forecast weekly sales data using R and `auto.arima`?

I have weekly sales data with for thousands of products which I want to forecast in an automated manner. What I clearly observe in my data is that there is a weekly skew within a month (wk1 sales < ...
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39 views

Time Series: Normality

I have a time serie, and I want a stationary process for search posible models. One of the requirments is normality. shapiro.test(serie) p-value = 0.0002322 How ...
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14 views

Is the following a standard HMM variant?

I have a problem that looks to me like a HMM variant. Could somebody confirm that I am on the right track modelling this and possibly tell me the name of this HMM variant if it is a standard HMM ...
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33 views

Financial time series data: Imputing before or after calculating returns?

I've got several time series of daily prices ($(p_t^j)_{t=1,\dots,n}$ ) of different tradable cards $j=1,\dots,k$. I'd like to calculate the time series of the (log)returns $r_t= ...
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12 views

Recursive daily forecast [migrated]

I am doing a recursive one-step-ahead daily forecast with different time series models for 2010. For example: ...
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2answers
68 views

How to estimate real series from smoothed moving average?

Suppose I have an observed time series $y_t$, which I suspect has been smoothed out. It appears to be significant autocorrelation at lag 1 and 2, therefore I suppose that the observed series $y_t$ is ...
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1answer
25 views

What is the benefit of using repeated measures in a mixed model vs. running a general linear model on the average of the repeated measures?

I have a dataset with protein measured twice from the same individual at three different timepoints. The data also includes the mean protein measure (the mean of the two repeated measures) for each ...
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38 views

Regression on default data and backward extrapolation

Suppose that we have bankruptcy data representative for Small and Medium-sized enterprises in a country. We can therefore calculate default rates. Furthermore suppose that we found that GDP, ...
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9 views

Difference time-variant/invariant vs dynamic/static

What is the difference of the property of the system being time-variant or time-invariant and the property being dynamic or static? In [1] a dynamic system was defined as system where the output ...
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15 views

Period of a process using spectral density

How can I determine the period of the process from the given spectral density function: $ S_X ( \omega ) = \frac{1}{1-1.8\cos (6 \omega )+0.81} $ I know that it's a simple one but I somehow struggle ...
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13 views

Optimal grouping in one dimensional data with constraints [duplicate]

I have a 1d series of data with of approximately 100 values. I would like to partition series into 1, 2 or 3 groups, depending on the proximity of the values. What statistical technique would work ...
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1answer
73 views

Cross Correlation and Prewhitening

I am using cross correlation to demonstrate a potential link between two time series (ext & co). Both series are strongly autocorrelated, so it is difficult to assess the dependence between the ...
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1answer
31 views

Why does this condition on AR coefficients imply a unit root?

Consider an AR($q$) process: $$ X_t-\theta_1 X_{t-1}-...-\theta_q X_{t-q}=Z_t $$ where $Z_t$~$WN(0,1)$. Why does the following condition on the process's coefficients imply a unit root: $$ ...
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35 views

Unit roots Dickey Fuller test question

I've been searching in bibliography about this test applied to an ARMA(p,q) model, and find out that every single book states the null hypothesis as "1 is a root of the operator". I was wondering if ...
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2answers
76 views

Regression and Time Series

I was posed a problem by a colleague that i am struggling with. He is interested in the relationship between 10 variables and a single dependent, continuous variable. This could simply be an OLS ...
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36 views

PCA/SVD with datetime fields

I have a dataset or flight data with several columns including delay time, and date of departure. There are several other parameters, and I would like to run some sort of PCA with SVD to see how ...
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1answer
39 views

Box Cox Transformation makes Out of sample Forecast Error worse?

I am doing a regression on time series data. I have 60 lagged predictors which I will call x to predict a continuous variable y. I used the BoxCox function from the forecast package to transform y and ...
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17 views

Time-series analysis of categorical data

I am attempting to look at nest attendance patterns in birds. I have a dataset looking at 5 nests, every 5 minutes I assessed whether the male=1, female=2, both birds=3 or no birds=4 were at each ...
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16 views

Example and simulated path of strict(ly) stationary process

There are many question on stationary process but very few related to strict stationary process. I am just looking for an example and simulated path of strict stationary process and how strict ...
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15 views

Matched pairs versus multiple t-test measurements for task performance over time

I am trying to compare performance on a task over time across one group based on initial performance, but am running into a little trouble. As background, I am examining a group of students' ...
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1answer
38 views

Granger causality - lag=1?

I have a question related to Granger Causality testing. Is it okay to use a lag-length of lag=1 in my Granger-test? The optimum lag length selection in my R ...
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66 views

What are the published methods to smooth a time series of weights?

I am looking for methods to smooth a time series of human weights, in particular I would like to know methods that are quoted or described in articles published in peer-reviewed journals. I am also ...
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1answer
36 views

amplitude and phase from the Fourier transform equation

This is a snapshot from some text I'm currently reading which aims to describe how the amplitude and phase of a seasonal cycle can be determined: I think I understand the text but I'm unsure when ...
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10 views

Automatic identification of time identifiers

Problem statement I would like to perform classification based on data in a relational database. Each prediction should be to a given $timestamp$. That means that in the model I can only use data ...
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52 views

Mitigate autocorrelation in time series with AR(2) process

I have a dataframe with 4000 companies and I have calculated a liquidity measure of each of the company in the dataframe. Liquidity is highly persistent. And my analysis shows that in these indiviual ...
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2answers
114 views

Time series with autoregressive distributed lags: Forecasting for future

I have daily data from last 2 years. I want to do ARIMAX and the regressor component being autoregressive distributed lag of the same variable. Since it has impact, along with dummy variables to ...
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1answer
35 views

Is there an unambiguous stationarity test for time series?

It seems to me that the time series plot, the correlograms (ACS, PACS) and the "autocorrelation check for residuals test" can all be subject to interpretation. (I am using SAS 9.4) Is there an ...
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17 views

How to write this ARIMA model mathematically? [duplicate]

I am trying to analyze a time series: I see a strong seasonal pattern, so from every value, I subtract the value from the same month the previous year (12 periods prior). Also, I am using 1 AR term ...
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14 views

How could we detect an irregular (error) component from the data?

How could we detect an irregular (error) component from the data? We are all know the every subset data we have several component, there are seasonal component, trend component and error component. ...
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9 views

Online Non-stationary Plateau Detection

I need to detect plateaus in time series data online (only using previous data). I only know that plateaus should exist. I plan to use a fixed window moving average and define plateau detection as the ...
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155 views

XG Boost vs Random Forest for Time Series Regression Forecasting

I am using R's implementation of XGboost and Random forest to generate 1-day ahead forecasts for revenue. I have about 200 rows and 50 predictors. (As I go further in time I have more data so more ...
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2answers
56 views

What algorithm should I try to predict number of tweets

Background I have been collecting data of each tweet being sent out for each article. The data is like this. created_at, user_id, article_id xxx, x, x y, y, y ...
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12 views

Dynamic Time Warping finds erroneous similarity between time series

I am implementing 1NN using DTW as the distance measurement. It finds erroneous similarity between two time series when they are actually not similar. To give an example, let's suppose a & b are ...
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12 views

Large negative error correction term in short-run dynamic analysis

Does it make sense to have a statistically significant error correction term of -1.999? The model has passed the necessary diagnostic and stability tests.  
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46 views

Cross correlation between 2 filtered time series

I have 2 band pass filtered time series for 30-90 day band I would like to understand the lagged correlation between these 2 series in this band. The issue is that autocorrelations exist in both ...
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1answer
49 views

Time series of variance

If the mean or total of a variable studied over time displays seasonality, should I expect that the variance of that variable should display seasonality similar to the mean? Why or why not? The data ...
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34 views

Time Series and Testing Auto Correlation

Consider the following asset pricing model: $$RET_t=0.621+1.414(M_t)+0.732(HML_t)+1.9349(SMB_t)+0.250(RET_{t-1}) $$ $$(0.077) \hspace{5mm} (4.141) \hspace{5mm} (3.242) \hspace{5mm} (3.294) ...
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38 views

Clustering of Line Graphs

I have a sample of line graphs (like the ones below), and I am trying to find the easiest way to cluster graphs with similar patterns. It would be great to be able to say something like "X% of graphs ...